A formal notation for reasoning could possibly solve some reasoning issues for LLMs. Perhaps something like Lojban or symbolic logic. We don't have a lot of data for it, but it might be possible to synthetically generate it.
On a dark note, I wonder if increasing AI reasoning capability could have dangerous results. Currently, LLMs are relatively empathetic, and seem to factor the complex human experience into it's responses. Would making LLMs more logical, cold, and calculating result in them stepping on things which humans care about?